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UID:ce37f4a9179d6b37271104f5a50a28bf
CATEGORIES:RSS discussion paper meetings
CREATED:20190819T143932
SUMMARY:Functional models for time-varying random objects
LOCATION:Royal Statistical Society, 12 Errol Street London EC1Y 8LX
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:\n\nPre-meeting (DeMO) at 3 pm\nChair & Speaker: Yoav Zemel\nAuthors: D
ubey and Müller\n\n\nAbout the event:\n\n\nSpeaker: Paromita Dubey and Hans
-Georg Müller(University of California at Davis, USA)\n\n\nFunctional data
analysis provides a popular toolbox of functional models for the analysis o
f samples of random functions that are real valued. In recent years, sample
s of time-varying object data such as time-varying networks that are not in
a vector space have been increasingly collected. These data can be viewed
as elements of a general metric space that lacks local or global linear str
ucture and therefore common approaches that have been used with great succe
ss for the analysis of functional data, such as functional principal compon
ent analysis, cannot be applied. We propose metric covariance, a novel asso
ciation measure for paired object data lying in a metric space (?, d) that
we use to define a metric autocovariance function for a sample of random ?-
valued curves, where ? generally will not have a vector space or manifold s
tructure. The proposed metric autocovariance function is non-negative defin
ite when the squared semimetric d2 is of negative type. Then the eigenfunct
ions of the linear operator with the autocovariance function as kernel can
be used as building blocks for an object functional principal component ana
lysis for ?-valued functional data, including time-varying probability dist
ributions, covariance matrices and time dynamic networks. Analogues of func
tional principal components for time-varying objects are obtained by applyi
ng Fréchet means and projections of distance functions of the random object
trajectories in the directions of the eigenfunctions, leading to real-valu
ed Fréchet scores. Using the notion of generalized Fréchet integrals, we co
nstruct object functional principal components that lie in the metric space
?. We establish asymptotic consistency of the sample-based estimators for
the corresponding population targets under mild metric entropy conditions o
n ? and continuity of the ?-valued random curves. These concepts are illust
rated with samples of time-varying probability distributions for human mort
ality, time-varying covariance matrices derived from trading patterns and t
ime-varying networks that arise from New York taxi trips.\n\n\nView and dow
nload preprints\n\n\nMembers, non-Members, all welcome.\n\n\n\n
CONTACT:This email address is being protected from spambots. You need JavaScript enabled to view it.
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DTSTAMP:20200704T134629Z
DTSTART;TZID=Europe/London:20191016T170000
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